Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
1140 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 1140 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C24×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#2847 | C2 | semidirect |
| 2. C23×#2075 | C2 | semidirect |
| 3. C23×#2033 | C2 | semidirect |
| 4. C23×#1999 | C2 | semidirect |
| 5. C23×#1779 | C2 | semidirect |
| 7. C22×D8×C23 | C22 | semidirect |
| 10. C2×C23×#107 | C22 | semidirect |
| 11. C2×C23×#102 | C22 | semidirect |
| 16. C23×#340 | C22 | semidirect |
| 17. C23×#340 | C22 | semidirect |
| 42. C24×C23 | D8 | semidirect |
| 68. #32706 | C23 | direct (N × H) |
| 97. #2847 | C2×C23 | semidirect |
| 98. #2075 | C2×C23 | semidirect |
| 99. #2033 | C2×C23 | semidirect |
| 100. #1999 | C2×C23 | semidirect |
| 101. #1779 | C2×C23 | semidirect |
| 119. C22×D8 | C22×C23 | semidirect |
| 122. C2×#107 | C22×C23 | semidirect |
| 123. C2×#102 | C22×C23 | semidirect |
| 128. #340 | C22×C23 | semidirect |
| 129. #340 | C22×C23 | semidirect |
| 156. C23 | #32706 | direct (N × H) |
| 160. C24 | D8×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2847 | 2 |
| C23×#2075 | 2 |
| C23×#2033 | 2 |
| C23×#1999 | 2 |
| C23×#1779 | 2 |
| #32706 | 23 |